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Assertion: If |vec(A)+vec(B)|=|vec(A)-ve...

Assertion: If `|vec(A)+vec(B)|=|vec(A)-vec(B)|`, then angle between `vec(A)` and `vec(B)` is `90^(@)`
Reason: `vec(A)+vec(B)= vec(B)+vec(A)`

A

If both assertion and reason are true and the reason is the correct explanation of the assertion.

B

If both assertion and reason are true but reason is not the correct explanation of the assertion

C

If assertion is true but reason is false.

D

If the assertion and reason both are false.

Text Solution

Verified by Experts

The correct Answer is:
B
`|vec(A) + vec(B)| = |vec(A) - vec(B)|`
`rArr A^(2) + B^(2) + 2AB cos theta= A^(2) + B^(2)- 2AB cos theta`
`rArr cos theta= 0 rArr theta= 90^(@)`
Also vector addition is commutative
`vec(A) + vec(B)= vec(B) + vec(A)`
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